When an analytical approach is not known or practical for solving a mathematical problem, the numerical approach can be useful in finding approximate solutions as close as possible to the exact one. This module introduces a selection of numerical methods for the solution of linear and nonlinear algebraic equations, and differential equations, for finding a function that interpolates a set of data, and for finding numerical values of derivatives and integrals.

For each numerical method, we will consider the error that results from using approximations and introduce some theories of quantifying the error, which then indicates the accuracy of a numerical solution. We also consider the efficiency of a numerical method, which tells how much computational resource is required for achieving a given accuracy. Students will learn and practice implementing some of the methods in MatLab codes.

Module aims

The aim of this module is to introduce students to a selection of numerical methods in terms of their derivation, their accuracy and efficiency and their implementation.

Learning outcomes

Attributes Developed

Demonstrate knowledge and literacy of the taught numerical methods;

K

For basic numerical methods, prove their convergence and error bounds, and demonstrate understanding of their efficiency;

KC

Derive and devise numerical schemes with specific details for a range of mathematical problems;

KCT

Apply the above knowledge to determine the most suitable numerical method(s) for a practical problem;

CPT

Implement some numerical Linear Algebra methods in Matlab code, and gain proficiency in basic programming structures and methodology that can be used for general coding purposes.

1 x 1 hour lab drop-in session every 2 weeks (weeks 2, 4, 6, 8, 10) to provide hands-on learning experience of implementing numerical methods in MATLAB codes. Students are given lab sheets and template codes in order to solve practical problems. Instructor and teaching assistant(s) provide real time guidance, and students can also discuss with peers.

Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate:

Understanding of and ability to derive, devise and analyse numerical methods.

Subject knowledge through the recall of key definitions, theorems and their proofs.

Analytical ability through the solution of unseen problems in the test and exam.

Practical skills of implementing numerical methods in MATLAB code, and ability to understand and interpret given code.

Thus, the summative assessment for this module consists of:

One two hour examination (three of four best answers contribute to exam mark) at the end of the Semester; worth 80% module mark.

One in-semester test; worth 20% module mark

Formative assessment and feedback

Students receive written feedback via a number of marked coursework assignments which include computation projects over an 11 week period. In addition, verbal feedback is provided by lecturer/teaching assistant at lab sessions.

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2017/8 academic year.